Current automated market makers over binary events suffer
from two problems that make them impractical. First, they are unable
to adapt to liquidity, so trades cause prices to move the same amount
in both thick and thin markets. Second, under normal circumstances,
the market maker runs at a deficit. In this paper, we construct a
market maker that is both sensitive to liquidity and can run at a
profit. Our market maker has bounded loss for any initial level of
liquidity and, as the initial level of liquidity approaches zero,
worst-case loss approaches zero. For any level of initial liquidity we
can establish a boundary in market state space such that, if the
market terminates within that boundary, the market maker books a
profit regardless of the realized outcome.
Joint work with Tuomas Sandholm, Dave Pennock (Yahoo! Research New
York) and Dan Reeves (Yahoo! Research New York).